Understanding Hyperbolas

Understanding Hyperbolas

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Practice Problem

Hard

CCSS
8.G.B.8, HSF-IF.C.7D, 8.G.B.7

Standards-aligned

Created by

Sophia Harris

FREE Resource

Standards-aligned

CCSS.8.G.B.8
,
CCSS.HSF-IF.C.7D
,
CCSS.8.G.B.7
This video tutorial explains how to graph a hyperbola given its equation in standard form. It covers identifying the transverse axis, finding the center and vertices, determining the conjugate axis, and sketching a rectangle to help draw the asymptotes. The tutorial also includes calculating the foci and deriving the equations of the asymptotes, culminating in graphing the hyperbola by incorporating all these elements.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What determines whether a hyperbola has a vertical or horizontal transverse axis?

The order of the terms in the equation

The sign of the coefficients

The degree of the polynomial

The presence of a constant term

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If the equation of a hyperbola is given as (x+2)^2/16 - (y-3)^2/9 = 1, what is the center of the hyperbola?

(2, -3)

(3, -2)

(-2, 3)

(-3, 2)

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you determine the vertices of a hyperbola with a vertical transverse axis?

By adding and subtracting 'a' from the y-coordinate of the center

By adding and subtracting 'b' from the x-coordinate of the center

By adding and subtracting 'b' from the y-coordinate of the center

By adding and subtracting 'a' from the x-coordinate of the center

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the length of the conjugate axis if 'b' is 4?

2

4

16

8

Tags

CCSS.8.G.B.7

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How can the foci of a hyperbola be found?

By using the equation c^2 = a^2 - b^2

By using the equation c^2 = a^2 + b^2

By using the equation c^2 = b^2 - a^2

By using the equation c^2 = a^2 * b^2

Tags

CCSS.8.G.B.8

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of 'c' if a^2 = 9 and b^2 = 16?

6

5

4

3

Tags

CCSS.8.G.B.8

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the slope of the asymptote with a positive slope for a hyperbola with a = 3 and b = 4?

3/4

-3/4

-4/3

4/3

Tags

CCSS.HSF-IF.C.7D

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